A382745 If k appears, 7*k does not.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85

Offset

1,2

Comments

Also numbers with an even number of 7's in their prime factorization.

Natural density 7/8.

Links

Jan Snellman, Table of n, a(n) for n = 1..8751

Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 24.

Formula

a(n) ~ (8/7)*n.

Example

7 is removed since 7 = 7*1, 14, 21, 28, 35, 42 are removed, but 49 remains.

Maple

q:= n-> is(irem(padic[ordp](n, 7), 2)=0):
select(q, [$1..85])[];  # Alois P. Heinz, Apr 04 2025

Mathematica

Select[Range[100], EvenQ[IntegerExponent[#, 7]] &] (* Amiram Eldar, Apr 04 2025 *)

Prog

(Python)
def ok(n):
    c = 0
    while n and n%7 == 0: n //= 7; c += 1
    return c&1 == 0
print([k for k in range(1, 86) if ok(k)]) # Michael S. Branicky, Apr 04 2025
(Python)
from sympy import integer_log
def A382745(n):
    def f(x): return n+x-sum((k:=x//7**m)-k//7 for m in range(0, integer_log(x, 7)[0]+1, 2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Apr 10 2025

Crossrefs

Cf. A003159, A007417, A382744, A382746.

Sequence in context: A172251 A286997 A391574 * A187396 A020659 A047304

Adjacent sequences: A382742 A382743 A382744 * A382746 A382747 A382748

Keyword

nonn,easy

Author

Jan Snellman, Apr 04 2025

Status

approved